DECONVOLUTION IS AN IMPORTANT TOOL IN PHYSIOLOGICAL SYSTEM ANALYSIS WHERE INPUTS ARE USUALLY NON-ACCESSIBLE TO MEASUREMENT. WE HAVE DESCRIBED THE DEVELOPMENT OF A NEW DECONVOLUTION METHOD TO DEAL WITH THE MAJOR CHALLENGES POSED BY THE TREATMENT OF PHYSIOLOGICAL TIME-SERIES: ILL-CONDITIONING; INFREQUENT AND NONUNIFORM SAMPLED MEASUREMENTS; NEED OF AD HOC EFFICIENT NUMERICAL ALGORITHMS; COMPUTATION OF REALISTIC CONFIDENCE INTERVALS; NON NEGATIVITY CONSTRAINTS. USING A STOCHASTIC EMBEDDING APPROACH A CLASSICAL REGULARIZATION METHOD (PHILLIPS-TIKHONOV) WAS REINTERPRETED WITHIN A PROBABILISTIC SETTING. THIS LED TO THE DERIVATION OF NEW CRITERIA FOR THE CHOICE OF THE REGULARIZATION PARAMETER BASED ON LIKELIHOOD MAXIMIZATION. WHEN OBSERVATIONS ARE INFREQUENTLY AND/OR NONUNIFORMLY SAMPLED, THE CONCEPT OF "VIRTUAL GRID" IS INTRODUCED AND A METHOD BASED ON THIS NOTION WERE PROPOSED. ANALYTICAL EXPRESSIONS TO COMPUTE CONFIDENCE INTERVALS ENCOMPASSING ALSO THE BIAS ERROR WERE OBTAINED. ALGORITHMS THAT ARE FAST AS WELL AS STORAGE-EFFICIENT WERE WORKED OUT. THE PROPOSED METHOD, TESTED ON BOTH BENCHMARK PROBLEMS AND REAL PHYSIOLOGICAL DATA, IS NOW IN REVISION FOR AUTOMATICA THIS YEAR WE HAVE PROCEEDED A FEW STEPS AHEAD WITH SOME THEORETICAL ASPECTS. IN PARTICULAR WE HAVE SHOWN THAT, ALTHOUGH THE ABOVE REGULARIZATION CRITERIA HAVE BEEN DERIVED UNDER NORMALITY ASSUMPTIONS, THEY ARE, IN SOME SENSE, ROBUST AGAINST DISTRIBUTION ASSUMPTIONS AND THEY ADMIT MEANINGFUL INTERPRETATIONS ALSO IN THE NON-GAUSSIAN CASE, IN THAT THEY IMPOSE CONSISTENCY BETWEEN THE UNBIASED ESTIMATES OF BOTH MEASUREMENT NOISE AND SIGNAL VARIANCES AND THE OPTIMAL VALUE OF THE REGULARIZATION PARAMETER. IN ADDITION, SINCE IF ONE DESIRES A CONFIDENCE INTERVAL WHICH ALSO ACCOUNTS FOR PARAMETER UNCERTAINTY ANALYTICAL EXPRESSIONS ARE NOT AVAILABLE, THERE IS THE NEED OF A MONTE CARLO SIMULATION. A PERCENTILE MONTE CARLO METHOD WAS EMPLOYED TO COMPUTE THE CONFIDENCE INTERVALS OF THE ESTIMATE OF INSULIN SECRETION RATE AFTER A GLUCOSE STIMULUS OBTAINED BY THE DECONVOLUTION OF A C-PEPTIDE CONCENTRATION TIME-SERIES. THE LATTER PROBLEM ALSO INCLUDED THE DEALT WITH INPUT NONSTATIONATITY, WHICH WAS FACED VIA SUITABLE STOCHASTIC MODELING OF INSULIN SECRETION RATE AFTER A GLUCOSE STIMULUS. AN R-01 HAS BEEN SUBMITTED TO SUPPORT THE FULL DEVELOPMENT AND IMPLEMENTATION OF THIS METHOD AS A MODELING TOOL IN SAAM II.